I would carry a 12x12' piece of 6 or 10 mil plastic.

Cut about four flexible branches about 10' long (or eight shorter ones and bind them together), arc them like a dome tent and anchor the ends and put the plastic over them. Pile snow all round the base on top of the plastic edges to hold it in place, let the snow accumulate.

I did this once when I first moved here (from SoCal to SNOW COUNTRY!). I pounded a piece of rebar into the ground and wiggled it to anchor the branches, but the ground wasn't frozen badly. Once some snow covered it, it really wasn't too bad, and the difference between inside and outside was especially better when the wind came up... it was almost warm by comparison.

Sue